Benvenuti in queste pagine dedicate a scienza ed arte. Amelia Carolina Sparavigna

Saturday, June 11, 2016

On precession

Polaris is the brightest star in the constellation Ursa Minor. Very close to the north celestial pole, it is currently the pole star. But Odysseus, the Greek king of Ithaca, and the ancient mariners, did not use this star for their voyages. Why? because of precession (cerchio che più tardi in cielo è torto).

a very detailed and clear discussion on precession, with illustrations,

Here I am adapting a part of this excellent discussion.

The Earth is like a spinning top. Then the Earth’s rotational axis gyrates, with a period of 26,000 years. This motion is called axial precession, or "precession of the equinoxes".  Precession occurs because the Sun's gravity induces torque, which pulls the Earth's equatorial bulge toward the ecliptic. 
The axis of precession is perpendicular to the ecliptic and is aligned with the ecliptic axis. This axis projects to two points, the north and south ecliptic poles, which are inclined 23.5º to the celestial poles.

Note that axial precession affects the direction of the Earth's axis, but it does not affect the angle of its tilt relative to the ecliptic. Thus, precession affects the time of year in which various constellations are visible. The precssion does not affect the axis tilt, which is constant, and so the seasons themselves continue just like they are now.

Our standard Gregorian calendar is based on the solar, or tropical year, the time it takes the Sun to return to the same equinox, which is defined by the direction of the Earth's axis relative to the Sun. Since the seasons are intrinsic to the tropical year, our Gregorian calendar is calibrated so that the March equinox always falls on either March 20 or 21. This forces the seasons to occur during the same months, regardless of precession. However, the stars visible in the evening will slowly change. Figure 1 (of the given link) shows the winter solstice in the north, with the constellation Taurus prominent at midnight. If the Earth's axis were pointing in the opposite direction, Taurus would still be prominent at midnight, but it would be the summer solstice. So, for the solar calendar, the seasons occur in the same months, but we view different constellations during those months.

Besides the axial precession of 26,000, there is also a small oscillation of the tilt. Taking approximately 41,000 years the tilt shifts from 22.1° to 24.5° and back again. Currently the Earth is tilted at 23.44 degrees,  decreasing. If we want to evaluate the effect of this tilt shift on the sunrise and sunset azimuths on solstices, for instance at the Newgrange latitude, for Newgrange passage tomb that was built 5,000 ago, the influence of the tilt on the sunrise azimuths on solstice is about a degree (see  http://stretchingtheboundaries.blogspot.it/2016/06/newgrange-and-axial-tilt.html )